scholarly journals The Efficiency of Some Shrinkage Estimators for Shape Parameter of the Pareto-Rayleigh Distribution

2022 ◽  
Vol 15 (2) ◽  
pp. 407-426
Author(s):  
Mehdi Balui ◽  
Einolah Deiri ◽  
Farshin Hormozinejad ◽  
Ezzatallah Baloui Jamkhaneh ◽  
◽  
...  
Keyword(s):  
Shape Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators

scholarly journals On double stage minimax-shrinkage estimator for generalized Rayleigh model

2016 ◽  
Vol 5 (1) ◽  
pp. 39 ◽  
Author(s):  
Abbas Najim Salman ◽  
Maymona Ameen
Keyword(s):  
Sample Size ◽  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimator ◽  
Squared Error ◽  
Expected Sample Size ◽  
Generalized Rayleigh Distribution ◽  
The Mean

<p>This paper is concerned with minimax shrinkage estimator using double stage shrinkage technique for lowering the mean squared error, intended for estimate the shape parameter (a) of Generalized Rayleigh distribution in a region (R) around available prior knowledge (a<sub>0</sub>) about the actual value (a) as initial estimate in case when the scale parameter (l) is known .</p><p>In situation where the experimentations are time consuming or very costly, a double stage procedure can be used to reduce the expected sample size needed to obtain the estimator.</p><p>The proposed estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y(<strong>×</strong>) and suitable region R.</p><p>Expressions for Bias, Mean squared error (MSE), Expected sample size [E (n/a, R)], Expected sample size proportion [E(n/a,R)/n], probability for avoiding the second sample and percentage of overall sample saved  for the proposed estimator are derived.</p><p>Numerical results and conclusions for the expressions mentioned above were displayed when the consider estimator are testimator of level of significanceD.</p><p>Comparisons with the minimax estimator and with the most recent studies were made to shown the effectiveness of the proposed estimator.</p>

scholarly journals Two Different Classes of Shrinkage Estimators for the Scale Parameter of the Rayleigh Distribution

2021 ◽  
Vol 19 (1) ◽  
pp. 2-21
Author(s):  
Talha Omer ◽  
Zawar Hussain ◽  
Muhammad Qasim ◽  
Said Farooq Shah ◽  
Akbar Ali Khan
Keyword(s):  
Simulation Study ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Rayleigh Distribution ◽  
Shrinkage Estimators ◽  
Unbiased Estimators ◽  
Squared Error ◽  
The Mean ◽  
Simulation Results

Shrinkage estimators are introduced for the scale parameter of the Rayleigh distribution by using two different shrinkage techniques. The mean squared error properties of the proposed estimator have been derived. The comparison of proposed classes of the estimators is made with the respective conventional unbiased estimators by means of mean squared error in the simulation study. Simulation results show that the proposed shrinkage estimators yield smaller mean squared error than the existence of unbiased estimators.

Dependence of Shape Parameter of Weibull Distribution on Wave Spectral Width and Nonlinearity

2008 ◽  
Author(s):  
Changliang Li ◽  
Bingchen Liang ◽  
Lin Zhao
Keyword(s):  
Weibull Distribution ◽  
Wave Height ◽  
Shape Parameter ◽  
Wave Train ◽  
Spectral Width ◽  
Rayleigh Distribution ◽  
Height Distribution ◽  
Irregular Wave ◽  
Wave Height Distribution ◽  
Ocean Environment

In practice, the wave height distribution associated with an irregular wave train is always mathematically modeled as a Rayleigh distribution. However, the realistic ocean wave height distribution might deviate from a Rayleigh distribution. The present study demonstrates that a better mathematical model for wave height distribution under realistic ocean environment is a Weibull distribution. In comparison with a Rayleigh distribution, a Weibull distribution has the flexibility on choosing its “shape parameter”. According to the nonlinear Monte Carlo simulations, this study investigates the nonlinearity and spectral width effects on the shape parameter for the Weibull wave height distribution. A new empirical formula for calculating the shape parameter is proposed, which can be used easily in application.

scholarly journals Bayesian estimation of the shape parameter of generalized Rayleigh distribution under non-informative prior

2015 ◽  
Vol 4 (1) ◽  
pp. 1
Author(s):  
Yakubu Aliyu ◽  
Abubakar Yahaya
Keyword(s):  
Bayesian Estimation ◽  
Loss Function ◽  
Shape Parameter ◽  
Rayleigh Distribution ◽  
Skewed Distribution ◽  
Time Data ◽  
Squared Error Loss Function ◽  
Squared Error ◽  
Informative Prior ◽  
Generalized Rayleigh Distribution

<p>A decade ago, two-parameter Burr Type X distribution was introduced by Surles and Padgett [14] which was described as Generalized Rayleigh Distribution (GRD). This skewed distribution can be used quiet effectively in modelling life time data. In this work, Bayesian estimation of the shape parameter of GRD was considered under the assumption of non-informative prior. The estimates were obtained under the squared error, Entropy and Precautionary loss functions. Extensive Monte Carlo simulations were carried out to compare the performances of the Bayes estimates with that of MLEs. It was observed that the estimate under the Entropy loss function is more stable than the estimates under squared error loss function, Precautionary loss function and MLEs.</p>

scholarly journals Preliminary test shrinkage estimators for the shape parameter of generalized exponential distribution

2016 ◽  
Vol 5 (4) ◽  
pp. 162
Author(s):  
Abbas Najim Salman ◽  
Rana Hadi
Keyword(s):  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Preliminary Test ◽  
Shrinkage Estimators ◽  
Generalized Exponential Distribution ◽  
Initial Value ◽  
Squared Error ◽  
Optimal Region ◽  
Past Experiences

The present paper deals with the estimation of the shape parameter α of Generalized Exponential GE (α, λ) distribution when the scale parameter λ is known, by using preliminary test single stage shrinkage (SSS) estimator when a prior knowledge available about the shape parameter as initial value due past experiences as well as optimal region R for accepting this prior knowledge.The Expressions for the Bias [B (.)], Mean Squared Error [MSE] and Relative Efficiency [R.Eff (.)] for the proposed estimator is derived.Numerical results about conduct of the considered estimator are discussed include study the mentioned expressions. The numerical results exhibit and put it in tables.Comparisons between the proposed estimator  withe classical estimator  as well as with some earlier studies were made to show the effect and usefulness of the considered estimator.

A family of shrinkage estimators for Weibull shape parameter in censored sampling

2006 ◽  
Vol 49 (3) ◽  
pp. 513-529 ◽  
Author(s):  
Housila Prasad Singh ◽  
Sharad Saxena ◽  
Harshada Joshi
Keyword(s):  
Shape Parameter ◽  
Shrinkage Estimators ◽  
Censored Sampling

scholarly journals Pretest shrinkage estimators for the shape parameter of a Pareto model using prior point knowledge and record observations

2017 ◽  
Vol 14 (1) ◽  
Author(s):  
Leila Barmoodeh ◽  
Mehran Naghizadeh Qomi
Keyword(s):  
Unbiased Estimator ◽  
Shape Parameter ◽  
Shrinkage Estimators ◽  
Numerical Example ◽  
Scale Parameters ◽  
Error Loss ◽  
Pareto Model

Considering a Pareto model with unknown shape and scale parameters \(\alpha\) and \(\beta\), respectively, we are interested in Thompson shrinkage test estimation for the shape parameter \(\alpha\) under the Squared Log Error Loss (SLEL) function. We find a risk-unbiased estimator for \(\alpha\) and compute its risk under the SLEL. According to Thompson (1986), we construct the pretest shrinkage (PTS) estimators for \(\alpha\) with the help of a point guess value \(\alpha_0\) and record observations. We investigate the risk-bias of these estimators and compute their risks numerically. A comparison is performed between the PTS estimators and a risk-unbiased estimator. A numerical example is presented for illustrative and comparative purposes. We end the paper by discussion and concluding remarks.

scholarly journals Employ Shrinkage Estimation Technique for the Reliability System in Stress-Strength Models: special case of Exponentiated Family Distribution

2020 ◽  
Vol 33 (4) ◽  
pp. 50
Author(s):  
Eman A.A. ◽  
Abbas N .S.
Keyword(s):  
Shape Parameter ◽  
Mean Squared Error ◽  
Scale Parameter ◽  
Estimation Methods ◽  
Shrinkage Estimation ◽  
Shrinkage Estimators ◽  
Strength Model ◽  
Squared Error ◽  
Strength Models ◽  
Special Case

       A reliability system of the multi-component stress-strength model R(s,k) will be considered in the present paper ,when the stress and strength are independent and non-identically distribution have the Exponentiated Family Distribution(FED) with the unknown  shape parameter α and known scale parameter λ  equal to two and parameter θ equal to three. Different estimation methods of R(s,k) were introduced corresponding to Maximum likelihood and Shrinkage estimators. Comparisons among the suggested estimators were prepared depending on simulation established on mean squared error (MSE) criteria.

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